Linear programs are a mathematical formulation of problems, such as resource allocation. Resource allocation issues are extremely widespread, and can be found in manufacturing, services, construction, computer network management and many other areas. Accordingly, intense research activity has been devoted to developing algorithms to solve linear programs, and several major steps forward have been made. In particular, the Simplex method developed in 1947 and the more recent Perceptron method have achieved some success in providing solutions.
However, when applied to some linear programming applications, known methods may encounter circumstances in which progress toward a solution is slowed or prevented. Additionally, use of known methods may result in degraded performance due to the size of some linear programs, which may involve hundreds of thousands of variables and constraints. Accordingly, more advanced linear programming algorithms are needed, which will provide solutions when existing methods result in failure or delay.